I don’t think you can get away from discussing about the meanings of concurrency and parallelism and how they relate to each other. Unfortunately. In my view they are two different things, though not necessarily unrelated.
I see concurrency as property of the problem or your solution to the problem. Splitting your system into multiple processes which communicate with each by messages can just be a very nice and practical way of describing the problem and hence the solution. For example if you are doing a server which has to handle multiple connections then structuring the system so that each connection has its own set of independent processes can be a very nice way of building the system.
Parallelism however, I see as a property of the underlying hardware. It is that which determines how many things I can actually do in parallel at the same time. Then it is up to me to design my system so that it can actually use this parallelism.
That is my view anyway.
So Erlang/Elixir, the language, gives me a base and a set of primitives for building concurrent systems. How I use it is up to me. The BEAM implements this base and provides the concurrency which I can use when I design my system. It provides all the processes, communication and error handling etc. It also uses the parallelism provided by the underlying system to run my concurrent processes in parallel where possible. So if it has access to six cores it can do six things at the same time, if your system design allows it.
Now things start getting tricky and we can show that concurrency and parallelism are different things. At least from my point of view.
Here is a simple examples. Suppose we build a ring processes where we can send messages around the ring. So if I send a message to the first process and the message will be sent from process to process around the the ring and finally come back to the original sender. Now we build a ring with 1000000 processes around which I will send 1000000 messages. That is a lot of concurrency!
Now I build my system so that it sends messages around the ring one message at a time, so it sends a message waits for it to go around the ring and then sends the next message and so on for all the 1000000 messages. How much parallelism do we actually have? Very little in fact. We have a very concurrent system which is basically sequential where any underlying parallelism won’t be usable.
So the language provides the concurrency, and the BEAM can provide the parallelism but it is up to you to design your system in such a way as to use this parallelism.
Sorry this became much longer than I had planned.